Above the united states in that rank (and by a LOT) is most of Europe. France, Belgium, Austria, most of Eastern Europe (and the Netherlands if you were to add "self" chosen euthanasia to suicide figures, bringing it up to over 20. Self between brackets since it's often not a choice, as medical treatments are stopped for elderly people in Holland, making euthanasia the only treatment that can offer hope to alleviate pain)
There's also Japan, just in the top10, which was claimed to have a lower suicide rate than the US because of lack of guns, in fact has a suicide rate just short of twice that of the US.
Incidentally, all muslim nations are reporting suicide rates that I just can't believe are accurate, or they're just not present at all. I know multiple stories about suicide from people in Kuwait, and I've never been (just work with consultants that have been there). Presumably they only report suicides amongst Kuwaiti, not the 80% immigrant population, and even then it seems on the low side.
There's reasons for suicide, but merely having an easy means to do it (guns) doesn't factor in at all. Looking at that list, clearly the cold is the main factor, with a close second bad economic conditions, and then we move on to lack of freedom. I wonder if you were to check suicide rates in parts of the US if this pattern would hold. Most in the poor northern states ?
Yep: http://www.suicide.org/suicide-statistics.html#death-rates (not sure if it's a good reference)
Alaska comes out on top, with only New Mexico as a southern state in the top-5.
So here's the theory from those statistics.
1) cold (maybe lack of sunlight ?) is a big cause of suicide
2) barring that, bad economic conditions
3) after that, bad government will do it